Improve check-style.py

I stumbled upon these issues while rebasing and fixing @jadahl's work for Add VR support under Wayland (#1743):

1. The script did not wait for the amend command to complete, which made it unusable in a multi-step rebase. Fixed this by using subprocess.run() instead of Popen().
2. New files were not checked and re-formatted. Fixed this by not turning off formatting when the chunk starts at line 1.

There are some other minor tweaks to improve the readability of the Python code.